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Spectra of linear fractional composition operators on the growth space and Bloch space of the upper half-plane. (English) Zbl 1508.47040

Summary: In this article, we provide a complete description of the spectra of linear fractional composition operators acting on the growth space and Bloch space over the upper half-plane. In addition, we also prove that the norm, essential norm, spectral radius and essential spectral radius of a composition operator acting on the growth space are all equal.

MSC:

47B33 Linear composition operators
30H30 Bloch spaces
47A10 Spectrum, resolvent
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